Convergence, boundedness, and ergodicity of regime-switching diffusion processes with infinite memory

2020 ◽  
Author(s):  
Jun Li ◽  
Fubao Xi
Keyword(s):  
Regime Switching ◽  
Diffusion Processes ◽  
Infinite Memory ◽  
Switching Diffusion

Permanence and extinction of stochastic regime-switching mutualism model

2020 ◽  
Vol 13 (04) ◽  
pp. 2050028
Author(s):  
Guangying Lv ◽  
Beibei Zhang
Keyword(s):  
Regime Switching ◽  
Diffusion Processes ◽  
Sufficient Conditions ◽  
Switching Diffusion ◽  
Random Switching ◽  
The Difference ◽  
Mutualism Model

This paper is concerned with the permanence and extinction of a stochastic regime-switching mutualism model. We aim to find the difference between the stochastic mutualism model with regime-switching and without regime-switching. By studying ergodicity of regime-switching diffusion processes, we establish the sufficient conditions to estimate the permanence and extinction of a species in a random switching environment. Moreover, compared with the system without switching, the advantages of the stochastic regime-switching mutualism model are given.

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